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Trazado el gráfico de la función/ ctg(x)*cos(x)

Gráfico de la función y = ctg(x)*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cot(x)*cos(x)
f(x)=cos⁡(x)cot⁡(x)f{\left(x \right)} = \cos{\left(x \right)} \cot{\left(x \right)} 
f = cos(x)*cot(x)
Gráfico de la función
80246-8-6-4-2-5000050000
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
cos⁡(x)cot⁡(x)=0\cos{\left(x \right)} \cot{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π2x_{1} = - \frac{\pi}{2}
x2=π2x_{2} = \frac{\pi}{2}
Solución numérica
x1=92.6769830369374x_{1} = 92.6769830369374
x2=−23.5619450140352x_{2} = -23.5619450140352
x3=−45.5530935939383x_{3} = -45.5530935939383
x4=17.2787587191641x_{4} = 17.2787587191641
x5=76.9690195630622x_{5} = 76.9690195630622
x6=48.6946858762043x_{6} = 48.6946858762043
x7=−73.8274272796526x_{7} = -73.8274272796526
x8=39.2699086835855x_{8} = 39.2699086835855
x9=−98.9601677364429x_{9} = -98.9601677364429
x10=−26.7035370683564x_{10} = -26.7035370683564
x11=−32.9867219511814x_{11} = -32.9867219511814
x12=73.8274274867432x_{12} = 73.8274274867432
x13=58.1194643607763x_{13} = 58.1194643607763
x14=89.5353909275596x_{14} = 89.5353909275596
x15=−92.676982818755x_{15} = -92.676982818755
x16=83.2522045003433x_{16} = 83.2522045003433
x17=−20.4203519762382x_{17} = -20.4203519762382
x18=−14.1371668348422x_{18} = -14.1371668348422
x19=−89.5353907537234x_{19} = -89.5353907537234
x20=−4.71238848455677x_{20} = -4.71238848455677
x21=10.9955738135239x_{21} = 10.9955738135239
x22=42.4115007257482x_{22} = 42.4115007257482
x23=7.85398174563321x_{23} = 7.85398174563321
x24=26.7035372957759x_{24} = 26.7035372957759
x25=−48.6946856519848x_{25} = -48.6946856519848
x26=−76.969019142094x_{26} = -76.969019142094
x27=51.836278906418x_{27} = 51.836278906418
x28=−64.4026491374242x_{28} = -64.4026491374242
x29=54.9778709800313x_{29} = 54.9778709800313
x30=−32.9867233536188x_{30} = -32.9867233536188
x31=36.1283159260006x_{31} = 36.1283159260006
x32=−54.9778719374446x_{32} = -54.9778719374446
x33=−1.57079643412171x_{33} = -1.57079643412171
x34=−54.9778705470218x_{34} = -54.9778705470218
x35=29.8451303260505x_{35} = 29.8451303260505
x36=14.1371671153205x_{36} = 14.1371671153205
x37=17.2787600994214x_{37} = 17.2787600994214
x38=−17.2787598652139x_{38} = -17.2787598652139
x39=−98.9601691056411x_{39} = -98.9601691056411
x40=67.5442423466955x_{40} = 67.5442423466955
x41=−10.9955733545245x_{41} = -10.9955733545245
x42=−58.1194639960073x_{42} = -58.1194639960073
x43=61.2610559072772x_{43} = 61.2610559072772
x44=10.9955752430018x_{44} = 10.9955752430018
x45=−48.6946870685899x_{45} = -48.6946870685899
x46=64.4026493057109x_{46} = 64.4026493057109
x47=−61.2610570263942x_{47} = -61.2610570263942
x48=98.960168145952x_{48} = 98.960168145952
x49=−39.2699084457792x_{49} = -39.2699084457792
x50=23.5619451851288x_{50} = 23.5619451851288
x51=76.9690210413954x_{51} = 76.9690210413954
x52=80.1106131287292x_{52} = 80.1106131287292
x53=−92.6769842647274x_{53} = -92.6769842647274
x54=95.8185760670326x_{54} = 95.8185760670326
x55=61.2610572679436x_{55} = 61.2610572679436
x56=−51.8362786889097x_{56} = -51.8362786889097
x57=−42.4115005568527x_{57} = -42.4115005568527
x58=−67.5442421738335x_{58} = -67.5442421738335
x59=−4.71238987596373x_{59} = -4.71238987596373
x60=83.2522058525039x_{60} = 83.2522058525039
x61=32.9867238414546x_{61} = 32.9867238414546
x62=−70.6858356661912x_{62} = -70.6858356661912
x63=98.9601696430262x_{63} = 98.9601696430262
x64=4.71238871530383x_{64} = 4.71238871530383
x65=1.57079660442153x_{65} = 1.57079660442153
x66=−10.9955747699649x_{66} = -10.9955747699649
x67=−7.85398149471446x_{67} = -7.85398149471446
x68=39.2699073135637x_{68} = 39.2699073135637
x69=86.3937978856968x_{69} = 86.3937978856968
x70=−80.1106125767207x_{70} = -80.1106125767207
x71=45.553093765886x_{71} = 45.553093765886
x72=32.9867223968539x_{72} = 32.9867223968539
x73=−76.9690205214496x_{73} = -76.9690205214496
x74=54.9778724408964x_{74} = 54.9778724408964
x75=−95.8185758679732x_{75} = -95.8185758679732
x76=−70.6858342354489x_{76} = -70.6858342354489
x77=−26.7035384718653x_{77} = -26.7035384718653
x78=−83.2522056070609x_{78} = -83.2522056070609
x79=−36.1283154153854x_{79} = -36.1283154153854
x80=70.6858344565908x_{80} = 70.6858344565908
x81=20.4203521458051x_{81} = 20.4203521458051
x82=−29.8451300946099x_{82} = -29.8451300946099
x83=−86.3937977179549x_{83} = -86.3937977179549
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en cot(x)*cos(x).
cos⁡(0)cot⁡(0)\cos{\left(0 \right)} \cot{\left(0 \right)}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(cos⁡(x)cot⁡(x))y = \lim_{x \to -\infty}\left(\cos{\left(x \right)} \cot{\left(x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(cos⁡(x)cot⁡(x))y = \lim_{x \to \infty}\left(\cos{\left(x \right)} \cot{\left(x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cot(x)*cos(x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(cos⁡(x)cot⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)} \cot{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(cos⁡(x)cot⁡(x)x)y = x \lim_{x \to \infty}\left(\frac{\cos{\left(x \right)} \cot{\left(x \right)}}{x}\right)
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
cos⁡(x)cot⁡(x)=−cos⁡(x)cot⁡(x)\cos{\left(x \right)} \cot{\left(x \right)} = - \cos{\left(x \right)} \cot{\left(x \right)}
- No
cos⁡(x)cot⁡(x)=cos⁡(x)cot⁡(x)\cos{\left(x \right)} \cot{\left(x \right)} = \cos{\left(x \right)} \cot{\left(x \right)}
- No
es decir, función
no es
par ni impar
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